(24)(39)=(x+6)(2x-4)

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Solution for (24)(39)=(x+6)(2x-4) equation: 


Simplifying
(24)(39) = (x + 6)(2x + -4)

Multiply 24 * 39
936 = (x + 6)(2x + -4)

Reorder the terms:
936 = (6 + x)(2x + -4)

Reorder the terms:
936 = (6 + x)(-4 + 2x)

Multiply (6 + x) * (-4 + 2x)
936 = (6(-4 + 2x) + x(-4 + 2x))
936 = ((-4 * 6 + 2x * 6) + x(-4 + 2x))
936 = ((-24 + 12x) + x(-4 + 2x))
936 = (-24 + 12x + (-4 * x + 2x * x))
936 = (-24 + 12x + (-4x + 2x2))

Combine like terms: 12x + -4x = 8x
936 = (-24 + 8x + 2x2)

Solving
936 = -24 + 8x + 2x2

Solving for variable 'x'.

Combine like terms: 936 + 24 = 960
960 + -8x + -2x2 = -24 + 8x + 2x2 + 24 + -8x + -2x2

Reorder the terms:
960 + -8x + -2x2 = -24 + 24 + 8x + -8x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
960 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
960 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
960 + -8x + -2x2 = 0 + 2x2 + -2x2
960 + -8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
960 + -8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(480 + -4x + -1x2) = 0

Factor a trinomial.
2((20 + -1x)(24 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20

Subproblem 2
Set the factor '(24 + x)' equal to zero and attempt to solve:

Simplifying
24 + x = 0

Solving
24 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-24' to each side of the equation.
24 + -24 + x = 0 + -24

Combine like terms: 24 + -24 = 0
0 + x = 0 + -24
x = 0 + -24

Combine like terms: 0 + -24 = -24
x = -24

Simplifying
x = -24
Solution
x = {20, -24}

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